Oh you mean the actual chat application named 'Ajax Chat', No you can't as it requires adding files to the server I believe. If you know about CORS (or research it well) you could host the necessary files elsewhere. But even then it can't integrate with your forum.

Its my modification of the forumotion chatbox. It has sounds for sending and receiving messages, which the user can choose to turn off. It has private messaging, an online count, and even the ability to save conversations